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## Simple Interest

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

In this lesson, you will be introduced to the concept of borrowing money and the simple interest that is derived from borrowing. You will also be introduced to terms such as principal, amount, rate of interest, and time period. Through these terms, you can calculate simple interest using the simple interest formula.

## What is Simple Interest?

Simple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle. When we invest our money in any bank, the bank provides us interest on our amount. The interest applied by the banks is of many types one of them is simple interest.** **Now, before going deeper into the concept of simple interest, let’s first understand what is the meaning of a loan.

A loan is an amount that a person borrows from a bank or a financial authority to fulfill their needs. Loan examples include home loans, car loans, education loans, and personal loans. A loan amount is required to be returned by the person to the authorities on time with an extra amount, which is usually the interest you pay on the loan.

## Simple Interest Formula

Simple interest is calculated with the following formula: **S.I. = P × R × T, **where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

**Principal:**The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.**Rate:**Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.**Time:**Time is the duration for which the principal amount is given to someone. Time is denoted by T.**Amount:**When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.

**Amount = Principal + Simple Interest**

A = P + S.I.

A = P + PRT

A = P(1 + RT)

### Simple Interest Example:

Michael’s father had borrowed $1,000 from the bank and the rate of interest was 5%. What would the simple interest be if the amount is borrowed for 1 year? Similarly, calculate the simple interest if the amount is borrowed for 2 years, 3 years, and 10 years?

**Solution:**

Principal Amount = $1,000, Rate of Interest = 5% = 5/100. (Add a sentence here describing the given information in the question.)

Simple Interest | |

1 Year | S.I = (1000 ×5 × 1)/100 = 50 |

2 Year | S.I = (1000 × 5 × 2)/100 = 100 |

3 Year | S.I = (1000 ×5 × 3)/100 = 150 |

10 Year | S.I = (1000 × 5 × 10)/100 = 500 |

Now, we can also prepare a table for the above question adding the amount to be returned after the given time period.

SimpleInterest | Amount | |

1 Year | S.I = (1000 ×5 × 1)/100 = 50 | A= 1000 + 50 = 1050 |

2 Year | S.I = (1000 ×5 × 2)/100 = 100 | A= 1000 + 100 = 1100 |

3 Year | S.I = (1000 × 5 × 3)/100 = 150 | A = 1000 + 150 = 1150 |

10 Year | S.I = (1000 × 5 × 10)/100 = 500 | A = 1000 + 500 = 1500 |

## What Types of Loans use Simple Interest?

Most banks these days apply compound interest on loans because in this way banks get more money as interest from their customers, but this method is more complex and hard to explain to the customers. On the other hand, calculations become easy when banks apply simple interest methods. Simple interest is much useful when a customer wants a loan for a short period of time, for example, 1 month, 2 months, or 6 months.

When someone goes for a short-term loan using simple interest, the interest applies on a daily or weekly basis instead of a yearly basis. Consider that you borrowed $10,000 on simple interest at a 10% interest rate per year, so this 10% a year rate divide into a rate per day which is equal to 10/365 = 0.027%. So you have to pay $2.73 a day extra on $10,000.

## Simple Interest vs Compound Interest

Simple interest and compound interest are two ways to calculate interest on a loan amount. It is believed that compound interest is more difficult to calculate than simple interest because of some basic differences in both. Let’s understand the difference between simple interest and compound interest through the table given below:

Simple Interest | Compound Interest |

Simple interest is calculated on the original principal amount every time. | Compound interest is calculated on the accumulated sum of principal and interest. |

It is calculated using the following formula: S.I.= P × R × T | It is calculated using the following formula: C.I.= P × (1+r)^{t }– P |

It is equal for every year on a certain principal. | It is different for every span of the time period as it is calculated on the amount and not principal. |

**Simple Interest: Tips and Tricks**

- To find the time period, the day on which money is borrowed is not taken into account, but the day on which money has to be returned is counted.
- The rate of interest is the interest on every $100 for a fixed time period.
- Interest is always more in the case of compound interest as compared to simple interest.
- The formula or methods to calculate compound interest is derived from simple interest calculation methods.
- Rate of interest is always kept in fractions in the formula.

**Think Tank:**

- What if a bank provides you an interest such that your money doubles every day, if you invested $1 on day 1, in how many days you will become a billionaire?
- Will you invest if a bank provides a negative rate of interest?

## Solved Examples on Simple Interest

**Example 1: **Robert purchased a car worth $48,000, he borrowed the money from the bank at 10% per annum for a period of 4 years. How much amount he has to pay after the period.

**Solution:**

The principal value for the car is $48,000, the rate of interest is 10% and the time period given is 4 years.

Using the formula for amount, A= P(1+RT), A= 48000 × (1 + 10/100 × 4)

A= 48000 × (1 + 2/5)

A= 48000 × 7/5

A= $67200

Therefore, Robert has to pay $67,200.

**Example 2: **If Maria borrowed a sum of $46,500 for a period of 21 months at 20% per annum, how much simple interest will she pay?

**Solution:**

The principal amount is $46,500 and the rate of interest is 20% = 20/100. The time period given is 21 months = 21/12 years. Using the formula for interest I = P ×R × T. I = 46500 × 20/100 × 21/12, so I = $16800.

Therefore, Maria is going to pay $16,800.

## FAQs on Simple Interest

### What is the Use of Simple Interest?

Simple interest is used in cases where the amount that is to be returned requires a short period of time. So, monthly amortization, mortgages, savings calculation, and education loans use simple interest.

### What are the Types of Simple Interest?

Simple interest is of two types ordinary simple interest and exact simple interest. In the ordinary simple interest, a year is considered of 360 days while calculating the interest while in exact simple interest a year is considered of 365 (or 366 days of a leap year) days. Both methods use the same formula to calculate simple interest.

### Are Home Loans Simple or Compound Interest?

Home loans take a long time to repay, so the interest added by the lender is usually a compound interest.

### Are Car Loans Simple or Compound Interest?

Car loans or auto loans use simple interest to calculate the interest. The borrower agrees to pay the money back, plus a flat percentage of the amount borrowed. But in case the borrower fails to repay the amount on time, the company or the lender may start charging compound interest.

### What is the Difference between Simple and Compound Interest?

Simple interest is the interest paid only on the principal, whereas, compound interest is the interest paid on both principal and interest compounded in regular intervals.

### How do you Calculate Simple Interest?

Simple Interest is calculated using the following formula: SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100. And the principal is the sum of money that remains constant for every year in the case of simple interest.

### How do I Calculate Simple Interest Monthly?

To calculate simple interest monthly, we have to divide the yearly interest calculated by 12. So, the formula for calculating monthly simple interest becomes (P × R × T) / (100 × 12).

## Simple Interest Equation (Principal + Interest)

A = P(1 + rt)

Where:

- A = Total Accrued Amount (principal + interest)
- P = Principal Amount
- I = Interest Amount
- r = Rate of Interest per year in decimal; r = R/100
- R = Rate of Interest per year as a percent; R = r * 100
- t = Time Period involved in months or years

From the base formula, A = P(1 + rt) derived from A = P + I and since I = Prt then A = P + I becomes A = P + Prt which can be rewritten as A = P(1 + rt)

Note that rate r and time t should be in the same time units such as months or years. Time conversions that are based on day count of 365 days/year have 30.4167 days/month and 91.2501 days/quarter. 360 days/year have 30 days/month and 90 days/quarter.

## Simple Interest Formulas and Calculations:

Use this simple interest calculator to find A, the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. Where r is in decimal form; r=R/100; r and t are in the same units of time.

The accrued amount of an investment is the original principal P plus the accumulated simple interest, I = Prt, therefore we have:

A = P + I = P + (Prt), and finally **A = P(1 + rt)**

- Calculate Total Amount Accrued (Principal + Interest), solve for A
- A = P(1 + rt)

- Calculate Principal Amount, solve for P
- P = A / (1 + rt)

- Calculate rate of interest in decimal, solve for r
- r = (1/t)(A/P – 1)

- Calculate rate of interest in percent
- R = r * 100

- Calculate time, solve for t
- t = (1/r)(A/P – 1)

## Formula for Simple Interest

Simple interest is calculated by multiplying the interest rate by the principal amount and the time period which is generally in years. The S.I. formula is given as:

Simple Interest (SI) = P × T × R ⁄ 100 |

After the calculation for S.I. is done, the principal has to be added to it to get the total amount that the borrower has to give or the lender will collect. This is called total amount and its formula is given as:

A = P + S.I. |

### Notations in S.I. Formula:

S.I. | Simple Interest |

P | Principal Amount |

A | Total Amount |

R | Rate of Interest |

T | Time (in Years) |

Using the above notations, the formula for S.I. becomes,

This formula can be used to find the missing parameters while calculating the interest or total amount. Thus, the reduced forms of this formula are:

To calculate the Interest, the formula becomes:

I = PTR/100

To calculate the Principal Amount, the formula is:

P = (I × 100) / RT

To find the rate of interest, the formula will be:

R = (I × 100)/ PT

R (in decimal ) = I/PT

Thus, the rate of interest in percent is given by:

R = R * 100

To get the time, formula is:

T = (I × 100) / PR

All these formulas can be used based on the information provided in different scenarios.

### Example Question Based on S.I. Formula

**Question: **Calculate the Simple Interest if the principal amount is Rs. 2000, the time period is 1 year and the rate is 10%. Also, calculate the total amount at the end of 1 year.

**Solution:**

According to the formula of simple interest we have,

S.I. = [(Principal (P) × Time (T) × Rate (r)) / 100]

So, from the above values,

S.I. = [(2000 × 1 × 10)] / 100

= 20000/100

=200

So, the simple interest at the end of 1 year will be Rs. 200.

For the amount after 1 year,

A = P + S.I.

So, A = 2000+200 = 2200

Hence, the total amount at the end of the given tenure (i.e. 1 year) will be Rs. 2200.

**Definition**

**Simple interest** is the cost of borrowing money without accounting for the effects of compounding. In other words, simple interest only applies to the principal amount.

## Definition and Examples of Simple Interest

Interest represents a fee you pay on a loan or income you earn on deposits.1 Simple interest is a way of measuring interest that does not account for multiple periods of interest payments or charges. The interest rate will only apply to the principal amount of the loan or investment—it won’t be affected by any interest accrued.2

For example, say you invest $100 (the principal) at a 5% annual rate for one year. The simple interest calculation is:

- $100 x .05 interest x 1 year = $5 simple interest earned after one year

Note that the interest rate (5%) appears as a decimal (.05). To do your own calculations, you will need to convert percentages to decimals. For example, to convert 5% into a decimal, divide five by 100 to get .05.

### Note

An easy trick for remembering this is to think of the word percent as “per 100.” You can convert a percentage into its decimal form by dividing it by 100. Or, just move the decimal point two spaces to the left.

If you want to calculate simple interest over more than one year, calculate the interest earnings using the principal from the first year, multiplied by the interest rate and the total number of years.

- $100 x .05 interest rate x 3 years = $15 simple interest for three years

## Formula to Calculate Simple Interest (SI)

Simple Interest (SI) is a way of calculating the amount of interest that is to be paid on the principal and is calculated by an easy formula, which is by multiplying the principal amount by the rate of interest and the number of periods for which the interest has to be paid.

Here, interest is calculated only on the amount initially invested, and there is no interest in interest as the case with compound interest formula. It finds its usage in car loans and other consumer loans extended by banks and financial institutions. Also, the interest paid on savings bank accounts and term deposits by banks is also based on simple interest.

### Examples

Example #1

**ABC lends $5000 at 10% per annum for five years. Calculate the simple interest and total amount due after five years.**

Principal: $5000

Interest Rate: 10% per annum

Time period (in years) = 5

So now we will do the calculation this using the simple interest equation i.e

- Simple Interest = Principal * Interest Rate * Time Period
- Simple Interest =$5000 * 10%*5
- =$2500

**Total Simple Interest for 5 years= $2500**

Amount due after five years=Principal + Simple Interest

- = $5000+$2500
**Amount due after five years = $7500.**

Example #2

**Ravi purchased a microwave oven from an electronics store priced at Rs 10000. He financed the same from its lender, HDFC bank. Details are as follows:**

loan amount: Rs 12000

loan period: 1 year

interest: 10% per annum

The frequency of payment: monthly

We can calculate the equated monthly amount in excel using the PMT function.

Accordingly, the EMI amount Ravi will have to pay comes out to rs 879.16 (which includes both interest and principal amount). We can observe from the below **amortization schedule of the mortgage** that the interest amount kept decreasing with each payment and the principal amount kept increasing; however, the monthly installment remained the same across the tenure of the loan.

**Important Points to Note when calculating simple interest:**

- The period must be in years. If the same is in a month, it should be converted into years as a fraction.
- The interest rate must be expressed annually, but if the period is less than a year, it must be adjusted for one year. For instance, if the interest rate is 12% per annum, but the problem pertains to the monthly interest rate, then it will be 1% (12%/12).

Example #3

Ram took a car loan of $500000 from HDBC Bank, where interest is payable at 10% for 24 months. The loan is to be repaid by making equal monthly payments of $23072.46 (calculated using the PMT function in Excel)

The Schedule of payments calculated using SI formula in excel is as follows:

Let’s understand the concept of SI formula in excel using one more industry example related to Certificate of Deposits (CD).

Example #4

ABC Bank subscribed to the certificate of deposits totaling $20000 issued by the government of India, which carries a 5% interest per annum. The certificate of deposits matures in 6 months.

Interest earned by ABC Bank on the certificate of deposits:

Simple Interest= Principal * Rate* Time period

Thus, ABC Bank will earn a total interest of $500 on the certificates of deposits on maturity, i.e., after six months.

### Relevance and Uses

- Simple interest finds its relevance in the way interest is calculated by Banks on the savings bank account and term deposits held by depositors. Banks normally calculate interest every quarter in savings and term deposits.
- Returns calculated under simple interest will always be less than returns calculated under compound interest as it ignores the concept of compounding.
- SI formula ensures that the interest portion is higher in the Initial years and subsequently reduced as the tenure of the loan progresses.
- It calculates interest on short-term loans like car loans, certificates of deposits and savings accounts, and term deposits.

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